Molecular orbitals deltahedral clusters

At the beginning of the 1970 s, although many molecular orbital calculations had been performed on individual borane and carborane clusters, no generalisations had been made which would result in a theoretical unification of the field. Initially most boranes were thought to adopt structures based on fragments of an icosahedron, but it later became apparent, as more borane clusters were structurally characterised, that other deltahedrally based structures were quite common70). Williams first elucidated a struc-... 

Three-dimensional polyhedral molecules such as the borane anions, B Hn , are characterised by a total of n -I- 1 skeletal electron pairs or 4 n -I- 2 valence electrons in total [33]. The isolobal analogy between the BH and ML3 fragments has provided a theoretical relationship between the borane and the transition metal cluster compounds [34]. A detailed analysis of the molecular orbitals of deltahedral transition metal clusters showed that they also have a total of n -h 1 bonding skeletal molecular orbitals, which is the same as that in the borane clusters, and 6 n orbitals that are either non-bonding or involved in the metal-ligand bonding. Therefore, such clusters are characterised by 14 n -I- 2 valence electrons in total. 

As indicated above, the irreducible representations spanned by the L and L" tangential molecular orbitals in closo deltahedral clusters may contain an odd number of selfconjugate representations. For example, for the tetrahedron FJ transforms as a, and the tangential molecular orbitals span the representations ti + e + t2- Since... 

In recent years the fundamental ideas of Huckel molecular orbital theory, the Huckel rule, and other aspects of aromaticity have been extended to polyhedral three-dimensional inorganic structures regarded as aromatic like the two-dimensional aromatic hydrocarbons. Such an extension of Huckel molecular orbital theory requires recognition of its topological foundations so that they can be applied to three-dimensional structures as well as two-dimensional structures. In this connection graph theoretical methods can be used to demonstrate the close analogy between the delocalized bonding in two-dimensional planar aromatic systems such as benzene and that in three-dimensional deltahedral boranes, and carboranes. Related ideas can be shown to be applicable for metal carbonyl clusters, bare post-transition metal clusters, and polyoxometallates. ... 

---